Landscape topography from grayscale image
Import an image with the Images as planes add-on, to create a plane with the same proportions as the image you want to use on the landscape.


Enter edit mode Tab, and subdivide your mesh.

(On version 2.7 press W)
Start with 100 subdivisions.
The number of subdivisions will be directly proportional with the level of detail for your displacement.

Exit Edit mode (Tab)
Add a displace modifier with the following settings: Direction Normal, Texture Coordinates UV (The UV map has been generated automatically when you use the import images as planes)


Assign the texture to be used with the displacement modifier.


Your plane will deform using the texture.

At this point you can subdivide further or add a subdivision surface modifier for better detail. To control the height on the deformation play with the Strength value on the displace modifier.

But be very careful with the subdivision modifier. It is quite easy to create a very large number of subdivisions, and that might push your system's performance to the edge or make it crash. Read:
Blender render crash when using subsurf modifiers.